Sub-microscopic objects imaged in conventional light microscopes appear as diffraction limited spots with a much greater width. The center of the spot can, however, be determined to a much greater accuracy allowing one to effectively bypass the resolution limit of the light microscope in the detection of sparse, point-like objects. We have analyzed the effects of various types of error on the achievable accuracy and derived limiting expressions that allow the optimization of the experimental apparatus to minimize the effects of the various noise contributions.